Atomic and Nuclear Physics: Structure, Decay and Half-Life
Atomic and nuclear physics: structure and radioactivity
An atom has a small, dense nucleus of protons and neutrons, surrounded by electrons. The atomic number Z is the number of protons and identifies the element; the mass number A is protons plus neutrons. Isotopes have the same Z but different numbers of neutrons. Ions form when atoms gain or lose electrons.
Radioactivity is the random, spontaneous decay of unstable nuclei. Alpha particles are helium nuclei: mass 4, charge +2, highly ionising but stopped by paper. Beta particles are fast electrons emitted when a neutron changes into a proton: charge −1, stopped by a few millimetres of aluminium. Gamma radiation is a high-energy electromagnetic wave: no mass or charge, weakly ionising, reduced by thick lead. In decay equations, mass numbers and atomic numbers must balance.
Half-life is the time for half the unstable nuclei in a sample to decay. After n half-lives, the remaining fraction is (1/2)ⁿ. Activity is measured in becquerels and falls with half-life; count rate also depends on distance, shielding and background radiation. Uses include sterilising equipment, tracing leaks, dating materials and cancer treatment; safety requires shielding, distance and limiting exposure time.
Traps: treating half-life as a fixed amount rather than a fixed time; subtracting half the original each time instead of halving the remainder; forgetting background count; and writing a beta decay equation without increasing the proton number by one.
Worked example: A sample of 80 g has a half-life of 5 days. After 20 days, n = 20/5 = 4 half-lives. Remaining mass = 80 × (1/2)⁴ = 80/16 = 5 g.